My research is primarily concerned with investigating properties of charged liquids using equilibrium classical statistical mechanics. The principal theoretical technique is a mean electrostatic approach, which is based on integral equation type closures. I have developed and applied, with colleagues, the Modified Poisson-Boltzmann (MPB) theory [1,13, 51, 89]* and the Symmetric Poisson-Boltzmann (SPB) theory [41, 51, 89]. The SPB overcomes the unsymmetrical distribution functions of the classical PB theory while the MPB treats both the exclusion volume term and the fluctuation term which are neglected in the PB theory. This MPB theory complements the Density Functional theory and the standard Hypernetted-Chain (HNC) and Mean Spherical Approximation (MSA) integral equations, and is easier to handle, both theoretically and numerically. Structural and/or thermodynamic properties have been calculated for (i) bulk electrolytes, (ii) planar, spherical and cylindrical diffuse electric double layers, (iii) cell models of polyelectrolytes.

The electrolyte model generally falls into two classes (a) discrete solute ions in a continuum solvent, and (b) discrete solute and solvent molecules. Both models have been treated. The majority of investigations have been with the primitive model (PM) of charged hard spheres in a dielectric continuum, type (a). Non-primitive models considered have been mixtures of charged hard spheres + dipolar hard spheres, or mixtures of charged and uncharged hard spheres. In the majority of cases of PM Monte-Carlo (MC) simulation results, the MPB is as successful as the standard HNC equation. For example:

(i) 1:1, 1:2 and 2:2 bulk electrolytes with either equal or unequal ionic radii [57].

(ii) The planar electric double layer (review: S.L.Carnie and G.M.Torrie, Adv. Chem. Phys., 56 (1984) 141) and the spherical electric double layer (L.Degreve and M.Lozada-Cassou, Mol. Phys., 86 (1995) 759).

Predictions/calculations made using the mean electrostatic approach in the last 15 years:

(1) Use of SPB and MPB theories to calculate individual activity coefficients for a PM electrolyte [54, 57].

(2) Spinodals and gas-liquid coexistence region of a PM electrolyte using the non-linear SPB and MPB theories [60,62,74]. The non-linear HNC equation cannot be solved in this coexistence region.

(3) Demonstration by the SPB theory that for a three component PM system an attraction, under certain conditions, can exist between like charged colloidal particles [56]. See [65] for MPB theory applied to this system.

(4) MPB structural properties of the electric double layer around an infinitely long isolated cylindrical polyelectrolyte for 1:2, 2:1, 2:2 salts [59]. Good agreement for 2:2 salts with HNC/MSA theory. The cylindrical cell model is treated in [63, 72].

(5) For the three component model in which one species is neutral, the SPB, MPB theories predict the "depletion effect" arising from the packing effect of the uncharged molecules [61, 65, 70, 71, 75, 83]. The MPB predictions are on a par with those of MC and HNC while SPB gives qualitative agreement with MC. A MPB analysis of this model for the electric double layer is given in [68]. The SPB and MPB theories can be solved for a greater range of parameters than the HNC theory.

(6) SPB treatment of a four component model [77, 78].

(7) Demonstration by MPB of the low temperature capacitance anomaly of the electric double layer [92, 93].

1. Relation of bulk MPB closure to standard (radial distribution function)Û (direct correlation function) integral equation closures [1, 51, 66, 89].

2. Numerical solution of bulk/double layer non-linear fluctuation potential problem [51].

3. Numerical solution of ion-dipole mixtures for PB and MPB theories [15, 32].

4. SPB and MPB analysis of PM critical region for three component mixtures.

5. Application of SPB and MPB theories to colloidal interactions [82, 83].

* only some key papers or recent papers referenced.

1. C.W.Outhwaite, ‘Extension of the Debye-Hückel theory of electrolyte solutions’, J.Chem.Phys., 50 (1969) 2277.

2. C.W.Outhwaite, ‘The linear extension of the Debye-Hückel theory of electrolyte solutions’, Chem.Phys.Letters, 5 (1970) 77.

3. C.W.Outhwaite, ‘A modified Poisson-Boltzmann equation in the double layer’, Chem.Phys.Letters, 7 (1970) 636.

4. C.W.Outhwaite, ‘Partial treatment of the fluctuation potential in the Debye-Hückel theory of electrolyte solutions’, Mol.Phys., 20 (1971) 705.

5. D.M.Burley, V.C.L.Hutson and C.W.Outhwaite, ‘Numerical solution of a modified Poisson-Boltzmann equation in electrolyte solution theory’, Chem.Phys.Letters, 9 (1971) 109.

6. D.M.Burley, V.C.L.Hutson and C.W.Outhwaite, ‘Calculation of the thermodynamic properties of electrolyte solutions using a modified Poisson-Boltzmann equation’, Mol.Phys., 23 (1972) 867.

7. D.M.Burley, V.C.L.Hutson and C.W.Outhwaite, ‘A treatment of the volume and fluctuation term in Poisson’s equation in the Debye-Hückel theory of strong electrolyte solutions’, Mol.Phys., 27 (1974) 225.

8. C.W.Outhwaite, ‘Higher order closures and potential problems in diffuse double layer and strong electrolyte solution theory’, Mol.Phys., 27 (1974) 561.

9. C.W.Outhwaite, ‘Comment on the second moment condition of Stillinger and Lovett’, Chem.Phys.Letters, 24 (1974) 73.

10. C.W.Outhwaite and M.M.Thomlinson, ‘Reformulation of the n^th order Poisson equation in strong electrolyte solution theory using the Kirkwood integral equations’, Chem.Phys.Letters, 25 (1974) 375.

11. C.W.Outhwaite, ‘Potential theory of strong electrolytes solutions using the Bogoliubov-Born-Green-Yvon integral equations’, Mol.Phys., 28 (1974) 217.

12. C.W.Outhwaite and V.C.L.Hutson, ‘The mean spherical model for charged hard spheres’, Mol.Phys., 29 (1975) 1521.

13. C.W.Outhwaite, ‘Equilibrium theory of electrolyte solutions’, Statistical Mechanics Vol. 2 (Specialist Periodical Reports) ed. K.Singer, The Chemical Society, London (1975) Chapter 3, 188-255.

14. C.W.Outhwaite, ‘Two comments on the mean spherical approximation solution for the restricted primitive model of an electrolyte solution’, Chem.Phys.Letters, 37 (1976) 383.

15. C.W.Outhwaite, ‘A treatment of solvent effects in the potential theory of electrolyte solutions’, Mol.Phys., 31 (1976) 1345.

16. C.W.Outhwaite, ‘The potential of mean force between two ions in a dipolar solvent’, Mol.Phys., 33 (1977) 1229.

17. C.W.Outhwaite, ‘Symmetric radial distribution functions in the potential theory of electrolyte solutions’, Chem.Phys.Letters, 53 (1978) 599.

18. S.Levine and C.W.Outhwaite, ‘A comparison of theories of the aqueous electric double layer at a charged plane interface’, J.C.S.Faraday II, 74 (1978) 1670; corrigendum ibid 76 (1980) 221.

19. C.W.Outhwaite, ‘A modified Poisson-Boltzmann equation in electric double layer theory based on the Bogoliubov-Born-Green-Yvon integral equations’, J.C.S.Faraday II, 74 (1978) 1214.

20. C.W.Outhwaite, L.B.Bhuiyan and S.Levine, ‘Calculation of the mean electrostatic potential in the electric double layer using the mean spherical approximation’, Chem.Phys.Letters, 64 (1979) 150.

21. M.M.Thomlinson and C.W.Outhwaite, ‘Numerical study of a modified BBGY integral equation for the primitive model of an electrolyte solution’, Mol.Phys., 38 (1979) 941.

22. L.B.Bhuiyan, C.W.Outhwaite and S.Levine, ‘Numerical solution of a modified Poisson-Boltzmann equation in electric double layer theory’, Chem.Phys.Letters, 66 (1979) 321.

23. C.W.Outhwaite, ‘The electric double layer capacitance for a hard sphere ion-dipole electrolyte in the mean field approximation’, Chem.Phys.Letters, 76 (1980) 619.

24. C.W.Outhwaite, L.B.Bhuiyan and S.Levine, ‘Theory of the electric double layer using a modified Poisson-Boltzmann equation’, J.C.S.Faraday II, 76 (1980) 1388.

25. C.W.Outhwaite, ‘A preliminary treatment of solute and solvent interactions in the diffuse part of the electric double layer’, Can.J.Chem., 59 (1981) 1854.

26. D.M.Burley, V.C.L.Hutson, C.W.Outhwaite and M.M.Thomlinson, ‘The MPB and BBGY potential theories for a 2:2 restricted primitive model electrolyte at low concentrations’, J.Chem.Phys., 75 (1981) 3159.

27. S.Levine, C.W.Outhwaite and L.B.Bhuiyan, ‘Statistical mechanical theories of the electric double layer’, J.Electroanal.Chem., 123 (1981) 105.

28. C.W.Outhwaite, L.B.Bhuiyan and S.Levine, ‘Variation of the diffuse layer potential drop with surface charge in the modified Poisson-Boltzmann theory’, Chem.Phys.Letters, 78 (1981) 413.

29. L.B.Bhuiyan, C.W.Outhwaite and S.Levine, ‘Numerical solution of a modified Poisson-Boltzmann equation for 1:2 and 2:1 electrolytes in the diffuse layer’, Mol.Phys., 42 (1981) 1271.

30. C.W.Outhwaite and L.B.Bhuiyan, ‘A further treatment of the exclusion volume term in the modified Poisson-Boltzmann theory of the electric double layer’, J.C.S.Faraday II, 78 (1982) 775.

31. M.M.Thomlinson and C.W.Outhwaite, ‘A modified Poisson-Boltzmann equation for a primitive model electrolyte with unequal ion sizes’, Mol.Phys., 47 (1982) 1113.

32. C.W.Outhwaite, ‘Towards a mean electrostatic potential treatment of an ion-dipole mixture or a dipolar system next to a plane wall’, Mol.Phys., 48 (1983) 599.

33. C.W.Outhwaite and L.B.Bhuiyan, ‘An improved modified Poisson-Boltzmann equation in electric double layer theory’, J.C.S.Faraday II, 79 (1983) 707.

34. C.W.Outhwaite, ‘Comments on the modified Poisson-Boltzmann theory for the electric double layer’, J.C.S.Faraday II, 79 (1983) 1315.

35. C.W.Outhwaite, ‘Comment on: Corrected Debye-Hückel theory of electrolyte solutions [S.Nordholm, J.Chem.Phys., 78 (1983) 5759]’, J.Chem.Phys., 80 (1984) 2985.

36. G.M.Torrie, J.P.Valleau and C.W.Outhwaite, ‘Electrical double layers VI. Image effects for divalent ions’, J.Chem.Phys., 81 (1984) 6296.

37. C.W.Outhwaite and L.B.Bhuiyan, ‘A modified Poisson-Boltzmann equation in electric double layer theory for a primitive model electrolyte with size asymmetric ions’, J.Chem.Phys., 84 (1986) 3461.

38. C.W.Outhwaite, ‘A modified Poisson-Boltzmann equation for the ionic atmosphere around a cylindrical wall’, J.C.S.Faraday II, 82 (1986) 789.

39. C.W.Outhwaite and L.B.Bhuiyan, ‘The MPB5 diffuse layer potential drop’, J.Chem.Phys., 85 (1986) 4206.

40. D.Bratko, L.B.Bhuiyan and C.W.Outhwaite, ‘On the thermodynamic consistency of the modified Poisson-Boltzmann equation in the electric double layer’, J.Phys.Chem., 90 (1986) 6248.

41. C.W.Outhwaite, ‘Numerical solution of a Poisson-Boltzmann theory for a primitive model electrolyte with size and charge asymmetric ions’, J.C.S.Faraday II, 83 (1987) 949.

42. C.W.Outhwaite, ‘Image effects for point ions in a molecular solvent next to a plane wall’, Mol.Phys., 63 (1988) 77.

43. L.B.Bhuiyan and C.W.Outhwaite, ‘A mean field analysis of an ion-dipole mixture next to a plane charged wall’, J.Phys.Chem., 93 (1989) 1526.

44. C.W.Outhwaite and M.Molero, ‘An ion-dipole mixture against a charged hard wall with specific adsorption’, J.C.S.Faraday II, 85 (1989) 1585.

45. M.Molero and C.W.Outhwaite, ‘A mean field analysis of an ion-dipole mixture against a charged hard wall with specific adsorption, 2 non-linear results’, J.C.S.Faraday Trans., 86 (1990) 35.

46. C.W.Outhwaite and M.Molero, ‘Another comment on the anomalous behaviour of the inner-layer capacity at low electrolyte concentrations’, J.Electroanal.Chem., 286 (1990) 239.

47. M.M.Martinez, L.B.Bhuiyan and C.W.Outhwaite, ‘The thermodynamic consistency in the symmetric Poisson-Boltzmann equation for primitive model electrolytes’, J.C.S.Faraday Trans., 86 (1990) 3383.

48. L.B.Bhuiyan, D.Bratko and C.W.Outhwaite, ‘Electric surface tension in the modified Poisson-Boltzmann approximation’, J.Phys.Chem., 95 (1991) 336.

49. C.W.Outhwaite and M.Molero, ‘A mean field analysis of an ion-dipole mixture against a charged hard wall with specific dipole adsorption: classification of differential capacity plots’, Electrochimica Acta., 36 (1991) 1685.

50. C.W.Outhwaite and L.B.Bhuiyan, ‘The electric double layer around an isolated spherical macroion’, Electrochimica Acta., 36 (1991) 1747.

51. C.W.Outhwaite, M.Molero and L.B.Bhuiyan, ‘Symmetric Poisson-Boltzmann and modified Poisson-Boltzmann theories’, J.C.S.Faraday Trans., 87 (1991) 3227.

52. C.W.Outhwaite and M.Molero, ‘Application of a symmetric Poisson-Boltzmann equation to electrolyte mixtures’, Chem.Phys.Letters, 184 (1991) 566.

53. C.W.Outhwaite and L.B.Bhuiyan, ‘A modified Poisson-Boltzmann analysis of the electric double layer around an isolated spherical macroion’, Mol.Phys., 74 (1991) 367.

54. M.Molero, C.W.Outhwaite and L.B.Bhuiyan, ‘Individual ionic activity coefficients from a symmetric Poisson-Boltzmann theory’, J.C.S.Faraday Trans., 88 (1992) 1541.

55. L.B.Bhuiyan, C.W.Outhwaite and D.Bratko, ‘Structure and thermodynamics of micellar solutions in the modified Poisson-Boltzmann theory’, Chem.Phys.Letters, 193 (1992) 203.

56. C.W.Outhwaite and M.Molero, ‘Effective interaction between colloidal particles using a symmetric Poisson-Boltzmann theory’, Chem.Phys.Letters, 197 (1992) 643.

57. C.W.Outhwaite, M.Molero and C.W.Outhwaite, ‘Primitive model electrolytes in the modified Poisson-Boltzmann theory’, J.C.S.Faraday Trans., 89 (1993) 1315; corrigendum ibid. 90 (1994) 2002.

58. L.B.Bhuiyan and C.W.Outhwaite, ‘A modified Poisson-Boltzmann treatment of an isolated cylindrical electric double layer’, in Condensed Matter Theories, Vol. 8, ed L.Blum and F.B.Malik, (New York, Plenum, 1993), 551.

59. L.B.Bhuiyan and C.W.Outhwaite, ‘The cylindrical electric double layer in the modified Poisson-Boltzmann theory’, Phil.Mag. B. 69 (1994) 1051.

60. L.B.Bhuiyan, C.W.Outhwaite, M.Molero and E.González-Tovar, ‘The primitive model of ionic fluids near its critical point in the Poisson-Boltzmann and modified Poisson-Boltzmann theories’, J.Chem.Phys., 100 (1994) 8301.

61. C.W.Outhwaite, L.B.Bhuiyan and V.Vlachy, ‘A symmetric Poisson-Boltzmann study of a three component macroion solution’, Mol.Phys., 83 (1994) 183.

62. E.González-Tovar and C.W.Outhwaite, ‘The gas-liquid co-existence region of a primitive model electrolyte in the mean electrostatic potential approach’, Mol.Phys., 83 (1994) 1273.

63. T.Das, D.Bratko, L.B.Bhuiyan and C.W.Outhwaite, ‘On the modified Poisson-Boltzmann theory for linear polyelectrolyte solutions’, J.Phys.Chem., 99 (1995) 410.

64. M.Lanza-Amaro, L.B.Bhuiyan and C.W.Outhwaite, ‘Micellar solutions with added salt. A Monte-Carlo and modified Poisson-Boltzmann study’, Mol.Phys., 86 (1995) 725.

65. L.B.Bhuiyan and C.W.Outhwaite, ‘Polyelectrolyte solutions using a three component mixture’, Mol.Phys., 87 (1996) 625.

66. C.W.Outhwaite, ‘Comments upon the relations between the mean electrostatic potential and the distribution functions for a single restricted primitive model electrolyte’, Mol.Phys., 87 (1996) 1039.

67. L.B.Bhuiyan, C.W.Outhwaite and J.R.C.Maarel, ‘Structure functions of rodlike DNA fragment and polystyrenesulfonate solutions in the modified Poisson-Boltzmann theory’, Physica, A231 (1996) 295.

68. S.Lamperski, C.W.Outhwaite and L.B.Bhuiyan, ‘A modified Poisson-Boltzmann analysis of the solvent primitive model electric double layer’, Mol.Phys., 87 (1996) 1049.

69. R.Andreu, M.Molero, J.J.Calvente, C.W.Outhwaite and L.B.Bhuiyan, ‘Application of the MPB theory to the analysis of the ion-free layer thickness’, Electrochimica Acta., 41 (1996) 2125.

70. V.Vlachy, L.B.Bhuiyan and C.W.Outhwaite, ‘Asymmetric electrolyte in mixture with a neutral component: effects of counterion charge’, Mol.Phys., 90 (1997) 553.

71. J.Rescic, V.Vlachy, L.B.Bhuiyan and C.W.Outhwaite, ‘Monte-Carlo simulation studies of electrolyte in mixture with a neutral component’, J.Chem.Phys., 107 (1997) 3611.

72. T.Das, D.Bratko, L.B.Bhuiyan and C.W.Outhwaite, ‘Polyelectrolyte solutions containing mixed valency ions in the cell model. A simulation and modified Poisson-Boltzmann study’, J.Chem.Phys., 107 (1997) 9197.

73. S.Lamperski and C.W.Outhwaite, 'Treatment of an ion-dipole mixture against a charged hard wall using a mean field theory with Percus-Yevick exclusion volume term', Electrochemical Society Proceedings, 97-17 (1997) 54.

74. A.K.Sabir, L.B.Bhuiyan and C.W.Outhwaite, ‘Influence of ion size and valence on classical ionic criticality’, Mol.Phys., 93 (1998) 405.

75. J.Rescic, V.Vlachy, L.B.Bhuiyan and C.W.Outhwaite, ‘Monte-Carlo simulations of a mixture of an asymmetric electrolyte and a neutral species’, Mol.Phys., 95 (1998) 233.

76. S.Lamperski and C.W.Outhwaite, ‘A non-primitive model for the electrode/electrolyte interface based on the Percus-Yevick theory. Analysis of the different molecular sizes, ion valences and electrolyte concentrations’, J.Electroanal.Chem., 460 (1999) 135.

77. A.K.Mukherjee, L.B.Bhuiyan, C.W.Outhwaite and D.Y.C.Chan, ‘A four component model for small colloidal particles in an aqueous electrolyte’, Langmuir, 15 (1999) 4940.

78. J.Rescic, V.Vlachy, C.W.Outhwaite, L.B.Bhuiyan and A.K.Mukherjee, ‘A Monte-Carlo simulation and symmetric Poisson-Boltzmann study of a four-component electrolyte mixture’, J.Chem.Phys., 111 (1999) 5514.

79. S.S.Zakharova, S.U.Egelhaaf, L.B.Bhuiyan, C.W.Outhwaite, D.Bratko and J.R.C.van der Maarel, ‘Multivalent ion-DNA interaction: neutron scattering estimates of polyamine distribution’, J.Chem.Phys., 111 (1999) 10706.

80. B.Hribar, V.Vlachy, L.B.Bhuiyan and C.W.Outhwaite, 'Ion distribution in cylindrical capillary as seen by the modified Poisson-Boltzmann theory and Monte-Carlo simulations', J.Phys.Chem., B104 (2000) 11522.

81. C.W.Outhwaite and S.Lamperski, 'A treatment of the exclusion volume term in the inhomogeneous Poisson-Boltzmann theory for an ion-dipole mixture', Condensed Matter Phys., 4 (2001) 739.

82. L.B.Bhuiyan and C.W.Outhwaite, 'Thermodynamics and phase separation of a de-ionized colloidal system in the symmetric Poisson-Boltzmann and mean spherical approximation theories', J.Chem.Phys., 116 (2002) 2650.

83. L.B.Bhuiyan, V.Vlachy and C.W.Outhwaite, 'Understanding polyelectrolyte solutions: macroion condensation with emphasis on the presence of neutral co-solutes', Int. Reviews in Phys.Chem., 21 (2002) 1.

84. S.Lamperski and C.W.Outhwaite, 'Exclusion volume term in the inhomogeneous Poisson-Boltzmann theory for high surface charge', Langmuir 18 (2002) 3423.

85. B.Hribar Lee, V.Vlachy, L.B.Bhuiyan, C.W.Outhwaite and M.Molero, 'Theory and simulation of electrolyte mixtures', Mol.Phys., 101 (2003) 2969.

86. S.Lamperski and C.W.Outhwaite, 'Differential capacitance of the Solvent Primitive Model diffuse layer using the inhomogeneous Poisson-Boltzmann theory with exclusion volume term', J.Electroanal.Chem., 567 (2004) 263.

87. L.B.Bhuiyan and C.W.Outhwaite, 'Symmetric Poisson-Boltzmann structural properties near the gas-liquid point of a de-ionized colloidal suspension', Physica A, 339 (2004) 199.

88. L.B.Bhuiyan and C.W.Outhwaite, 'Comparison of the modified Poisson-Boltzmann theory with recent Density Functional theory and Simulation results in the planar electric double layer', Phys.Chem.Chem.Phys., 6 (2004) 3467.

89. C.W.Outhwaite, 'A modified Poisson-Boltzmann approach to homogeneous ionic solutions', Condensed Matter Phys., 7 (2004) 719.

90. J.Rescic, V.Vlachy, L.B.Bhuiyan and C.W.Outhwaite, 'Theoretical study of catalytic effects in micellar solutions', Langmuir, 21 (2005) 481.

91. L.B.Bhuiyan and C.W.Outhwaite, 'Comparison of density functional and modified Poisson-Boltzmann structural properties for a spherical double layer', Condensed Matter Phys., 8 (2005) 287.

92. L.B.Bhuiyan, C.W.Outhwaite and D.Henderson, 'A modified Poisson-Boltzmann analysis of the capacitance behaviour of the electric double layer at low temperatures' J.Chem.Phys., 123 (2005) 034704.

93. L.B.Bhuiyan, C.W.Outhwaite and D.Henderson, 'The planar electric double layer for a restricted primitive model electrolyte at low temperatures', Langmuir, 22 (2006) 10630.

94. L.B.Bhuiyan, C.W.Outhwaite and D.Henderson, 'Some simulation and modified Poisson-Boltzmann theory results for the contact values of an electrolyte near a charged electrode', J.Electroanal.Chem., 607 (2007) 54.

95. L.B.Bhuiyan, C.W.Outhwaite, D.Henderson and M.Alawneh, 'A further Monte Carlo and modified Poisson-Boltzmann analysis of two recent results in the electric double layer theory', Bangladesh J.Phys., 4 (2007) 93.

96. L.B.Bhuiyan, C.W.Outhwaite, D.Henderson and M.Alawneh, 'A modified Poisson-Boltzmann theory and Monte Carlo simulation study of surface polarization effects in the planar diffuse double layer', Molec.Phys., 105 (2007) 1395.

97. C.W.Outhwaite and L.B.Bhuiyan, 'The modified Poisson-Boltzmann electric double layer capacitance for point ions at low temperatures', J.Electroanal.Chem., 609 (2007) 51.

98. M.Alawneh, D.Henderson, C.W.Outhwaite and L.B.Bhuiyan, 'The effect of dielectric polarization on anomalous temperature effects in the electrical double layer', Mol.Sim., 33 (2007) 1279.